where \(\sigma (\cdot )\)  denotes the logistic sigmoid function and \(||\)  denotes vector concatenation. Finally, a discrete adjacency matrix \(\mathbf {A}\)  is obtained via element-wise, differentiable sampling, i.e., \(\mathbf {A}_{ij} \sim \mathrm {Ber}(\theta _{ij})\) , using the Gumbel softmax trick [1]}, [2]}. Note that GTS uses the complete training partition to parameterize the adjacency matrix at each batch. This means that (i) the model can use information from the whole (training) time series at training time; (ii) the model cannot adjust the learned graph at test time; (iii) the number of parameters grows linearly with the length of the input timeseries, which could be improved by adding dilation or pooling to the convolutional encoder.
